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A123180 Even positions of Sylvester's sequence A000058; the denominators of the (greedy) Egyptian fraction expansion of Cahen's constant. 3
2, 7, 1807, 10650056950807, 12864938683278671740537145998360961546653259485195807 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Eugène Cahen, Note sur un développement des quantités numériques, qui présente quelque analogie avec celui en fractions continues, Nouvelles Annales de Mathématiques, Vol. 10 (1891), pp. 508-514.
Eric Weisstein's World of Mathematics, Cahen's Constant.
Wikipedia, Cahen's constant.
FORMULA
a(n) = a(n-1)*(a(n-1)-1)*(a(n-1)*(a(n-1)-1)+1)+1.
a(n) is approximately k^4^n with k = 1.5979102180318731783... (A077125). - Charles R Greathouse IV, Dec 12 2013
Sum_{n>=0} 1/a(n) = A118227. - Amiram Eldar, Mar 19 2024
MATHEMATICA
f[n_] := n*(n-1)*(n*(n-1)+1)+1; a[0] = 2; a[n_] := a[n] = f[a[n-1]]; Array[a, 5, 0] (* Amiram Eldar, Mar 19 2024 *)
PROG
(PARI) a(n)=if(n, my(k=a(n-1)); k*=k-1; k*(k+1)+1, 2) \\ Charles R Greathouse IV, Dec 12 2013
CROSSREFS
Sequence in context: A082891 A000653 A128847 * A138198 A358482 A320505
KEYWORD
easy,nonn,changed
AUTHOR
David Eppstein, Oct 03 2006
EXTENSIONS
a(4) from Charles R Greathouse IV, Dec 12 2013
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)